Well-posedness for a moving boundary model of an evaporation front in a porous medium

饱和度对多孔介质中蒸发驱动密度不稳定性的影响：数学与数值分析

Impact of saturation on evaporation-driven density instabilities in porous media: mathematical and numerical analysis

本研究通过线性稳定性分析和数值模拟，探讨了水饱和度对多孔介质蒸发驱动密度不稳定性的影响，并给出了预测不稳定性发生及其对盐浓度影响的判据。

Flat Fronts and Stability for the Porous Medium Equation

This work is concerned with the equation $ \partial_t ρ= Δ_x ρ^m $, $ m > 1 $, known as the porous medium equation. It shows stability of the pressure of solutions close to flat travelling wave fronts in the homogeneous Lipschitz sense that is in a way optimal for the treatment of the equation. This is the first result of this type and implies global regularity estimates for any number of derivatives of the pressure. Consequences include smoothness, analyticity in temporal and tangential directions, and analyticity of the interface between empty and occupied regions. In the course of the argum…

多孔介质蒸发建模的相场方法：建模与升尺度

A phase-field approach to model evaporation from porous media: Modeling and upscaling

本文通过引入蒸汽组分开发了一个多孔介质蒸发的相场模型，利用匹配渐近展开验证其可简化为尖锐界面模型，并通过数值算例证明其能捕捉蒸发过程，最终采用周期均匀化方法将其升尺度至 Darcy 尺度。

Stability analysis for combustion fronts traveling in hydraulically resistant porous media

We study front solutions of a system that models combustion in highly hydraulically resistant porous media. The spectral stability of the fronts is tackled by a combination of energy estimates and numerical Evans function computations. Our results suggest that there is a parameter regime for which there are no unstable eigenvalues. We use recent works about partially parabolic systems to prove that in the absence of unstable eigenvalues the fronts are convectively stable.

Multi-layer asymptotic solution for wetting fronts in porous media with exponential moisture diffusivity

We study the asymptotic behaviour of sharp front solutions arising from the nonlinear diffusion equation θ_t = (D(θ)θ_x)_x, where the diffusivity is an exponential function D(θ) = D_o exp(βθ). This problem arises for example in the study of unsaturated flow in porous media where θ represents the liquid saturation. For physical parameters corresponding to actual porous media, the diffusivity at the residual saturation is D(0) = D_o << 1 so that the diffusion problem is nearly degenerate. Such problems are characterised by wetting fronts that sharply delineate regions of saturated and unsaturate…

The Cauchy problem for a combustion model in porous media

We prove the existence of a global solution to the Cauchy problem for a nonlinear reaction-diffusion system coupled with a system of ordinary differential equations. The system models the propagation of a combustion front in a porous medium with two layers, as derived by J. C. da Mota and S. Schecter in Combustion fronts in a porous medium with two layers, Journal of Dynamics and Differential Equations, 18(3) (2006). For the particular case, when the fuel concentrations in both layers are known functions, the Cauchy problem was solved by J. C. da Mota and M. M. Santos in An application of the …